Problem: The following line passes through point $(3, -10)$ : $y = -9 x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(3, -10)$ into the equation gives: $-10 = -9 \cdot 3 + b$ $-10 = -27 + b$ $b = -10 + 27$ $b = 17$ Plugging in $17$ for $b$, we get $y = -9 x + 17$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${11}$ ${12}$ ${13}$ ${14}$ ${15}$ ${16}$ ${17}$ ${18}$ ${19}$ ${20}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${\llap{-}11}$ ${\llap{-}12}$ ${\llap{-}13}$ ${\llap{-}14}$ ${\llap{-}15}$ ${\llap{-}16}$ ${\llap{-}17}$ ${\llap{-}18}$ ${\llap{-}19}$ ${\llap{-}20}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${11}$ ${12}$ ${13}$ ${14}$ ${15}$ ${16}$ ${17}$ ${18}$ ${19}$ ${20}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${\llap{-}11}$ ${\llap{-}12}$ ${\llap{-}13}$ ${\llap{-}14}$ ${\llap{-}15}$ ${\llap{-}16}$ ${\llap{-}17}$ ${\llap{-}18}$ ${\llap{-}19}$ ${\llap{-}20}$ $(3, -10)$